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分享</span><i class="fas fa-chevron-down"></i></a><ul class="menus_item_child"><li><a class="site-page child" href="/myblog/Gallery/"><i class="fa-fw fas fa-images"></i><span> 照片</span></a></li><li><a class="site-page child" href="/myblog/music/"><i class="fa-fw fas fa-music"></i><span> 音乐</span></a></li><li><a class="site-page child" href="/myblog/movies/"><i class="fa-fw fas fa-video"></i><span> 视频</span></a></li></ul></div><div class="menus_item"><a class="site-page" href="/myblog/link/"><i class="fa-fw fas fa-link"></i><span> 友链</span></a></div><div class="menus_item"><a class="site-page" href="/myblog/about/"><i class="fa-fw fas fa-heart"></i><span> 关于</span></a></div></div><div id="toggle-menu"><a class="site-page" href="javascript:void(0);"><i class="fas fa-bars fa-fw"></i></a></div></div></nav></header><main class="layout" id="content-inner"><div id="post"><div id="post-info"><h1 class="post-title">数据结构(JAVA)第二天(tree)</h1><div id="post-meta"><div class="meta-firstline"><span class="post-meta-date"><i class="far fa-calendar-alt fa-fw post-meta-icon"></i><span class="post-meta-label">发表于</span><time class="post-meta-date-created" datetime="2019-11-20T07:02:21.000Z" title="发表于 2019-11-20 15:02:21">2019-11-20</time><span class="post-meta-separator">|</span><i class="fas fa-history fa-fw post-meta-icon"></i><span class="post-meta-label">更新于</span><time class="post-meta-date-updated" datetime="2023-09-07T09:44:01.896Z" title="更新于 2023-09-07 17:44:01">2023-09-07</time></span><span class="post-meta-categories"><span class="post-meta-separator">|</span><i class="fas fa-inbox fa-fw post-meta-icon"></i><a class="post-meta-categories" href="/myblog/categories/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84/">数据结构</a></span></div><div class="meta-secondline"><span class="post-meta-separator">|</span><span class="post-meta-pv-cv" id="" data-flag-title="数据结构(JAVA)第二天(tree)"><i class="far fa-eye fa-fw post-meta-icon"></i><span class="post-meta-label">阅读量:</span><span id="busuanzi_value_page_pv"><i class="fa-solid fa-spinner fa-spin"></i></span></span></div></div></div><article class="post-content" id="article-container"><h1 id="tree树形结构"><a href="#tree树形结构" class="headerlink" title="tree树形结构"></a>tree树形结构</h1><p><img src="/myblog/image/data-construction-tree.png"></p>
<ul>
<li><p>树的根部节点是没有父节点的.一颗树种最多一个根节点(图种A就是根节点)</p>
</li>
<li><p>父子之间的链接从节点边缘开始</p>
</li>
<li><p>一个没有子节点的节点被称为<em>叶子节点(leaf node)</em></p>
</li>
<li><p>子节点有共同的父系节点的称为<em>兄弟节点(siblings)</em> </p>
</li>
<li><p>如果存在一条根节点到 q 的路径并且 p 出现在此路径上,那么我们称 p 是 q 的祖先节点, q 是 p 的后代节点.例如图中:A,C,G就是K的祖先节点</p>
</li>
<li><p>所有的处于同一个给定深度的节点集我们称之为树的级别(level).根节点处于零级别.(B,C,D是同一个级别)</p>
</li>
<li><p>一个节点的深度是从根节点到这个节点的路径长度.(G的深度是2,A-C-G)</p>
</li>
<li><p>一个节点的高度是从这个节点到最深的节点的路径长度.一棵树的高度就是根节点到最深节点的路径长度.一个树只有一个根节点那么他的高度为零.(B的高度是2,B-F-J)</p>
</li>
<li><p>树的高度和深度在所有节点中都是最大的.对于一个给定的树,深度和高度返回相同的值.但是对于一些独立的节点,我们可能会得到不同的结果.</p>
</li>
<li><p>节点的大小就是包含本身以及所有后代节点的数量(C的大小就是3)</p>
</li>
<li><p>如果一个树中每个节点仅仅只有一个子节点(叶子节点除外),那么我们称这样的树为 <em>偏斜树(skew tree)</em>.如果每个节点仅仅只有左边子节点,那么我们称这样的树叫<em>左偏树(left skew tree)</em>.相似的,只有右边有子节点就叫做<em>右偏斜树(right skew tree)</em>.</p>
</li>
</ul>
<p><img src="/myblog/image/data-structure-tree-skew.png"></p>
<h2 id="二叉树-Binary-Trees"><a href="#二叉树-Binary-Trees" class="headerlink" title="二叉树(Binary Trees)"></a>二叉树(Binary Trees)</h2><p>如果每个节点没有子节点或一个子项或两个子项那么我们称这样的树为二叉树(Binary Trees).空树也是有效的二叉树.我们可以用一个根和两个不相交的二叉树(称为左,右根子树)来构成一个形象化的二叉树.如下图:<br><img src="/myblog/image/data-type-tree-binary.png"></p>
<h3 id="二叉树的类型"><a href="#二叉树的类型" class="headerlink" title="二叉树的类型"></a>二叉树的类型</h3><h4 id="严格二叉树-strict-Binary-tree"><a href="#严格二叉树-strict-Binary-tree" class="headerlink" title="严格二叉树(strict Binary tree)"></a><strong>严格二叉树(strict Binary tree)</strong></h4><p>二叉树被能够被称为严格二叉树那要看他的每个节点是否都存在两个子节点或者没有子节点.</p>
<p><img src="/myblog/image/strict-binary-tree.png"></p>
<h4 id="满二叉树-full-binary-tree"><a href="#满二叉树-full-binary-tree" class="headerlink" title="满二叉树(full binary tree)"></a><strong>满二叉树(full binary tree)</strong></h4><p>主要就是看数的所有节点是否有两个子节点并且所有的叶子节点都处于同一级别,满足这条件就称为满二叉树.</p>
<p><img src="/myblog/image/full-tree-binary.png"></p>
<h4 id="完全二叉树-complete-Binary-tree"><a href="#完全二叉树-complete-Binary-tree" class="headerlink" title="完全二叉树(complete Binary tree)"></a><strong>完全二叉树(complete Binary tree)</strong></h4><p>一个二叉树能够被称为完全二叉树那么需要满足:这棵树的所有的叶子节点处于高度h或者h-1并且在这个连续的数字中没有任何的丢失.<br><img src="/myblog/image/conplete-binary-tree.png"></p>
<h3 id="二叉树的结构"><a href="#二叉树的结构" class="headerlink" title="二叉树的结构"></a>二叉树的结构</h3><p>简单起见,定义二叉树的数据是整型的.一个节点有左右两个链接到子节点的指向和数据域.如下图:<br><img src="/myblog/image/binary-structural-node.png"></p>
<h3 id="二叉树的遍历"><a href="#二叉树的遍历" class="headerlink" title="二叉树的遍历"></a>二叉树的遍历</h3><p><strong>归为三类:</strong></p>
<ul>
<li><p>前序遍历(DLR-PreOrder Traversal) 先从当前节点数据开始,然后左子树,然后右子树</p>
</li>
<li><p>中序遍历(LDR-InOrder Traversal)  先从左子树开始,然后当前节点数据,然后右子节点</p>
</li>
<li><p>后序遍历(LRD-PostOrder Traversal) 先从左子树开始,然后右子节点,然后当前节点数据</p>
</li>
</ul>
<p><strong>还附加一类遍历</strong></p>
<ul>
<li>水平顺序遍历(Level Order Traversal): 这个方法是来自 <strong>Breadth First</strong> 遍历的启发(图表算法的BFS)</li>
</ul>
<p>一个例子分别用不同的遍历产生的结果:先假设一个二叉树如下图:</p>
<p><img src="/myblog/image/binary-tree-traversal.png"></p>
<p><strong>二叉树实体代码:</strong></p>
<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">@Data</span><br><span class="line">public class BinaryTreeNode &#123;</span><br><span class="line"></span><br><span class="line">    public int data;</span><br><span class="line">    public BinaryTreeNode left,right;</span><br><span class="line"></span><br><span class="line">    public BinaryTreeNode(int data) &#123;</span><br><span class="line">        this.data = data;</span><br><span class="line">        left = null;</span><br><span class="line">        right = null;</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

<p><strong>前序遍历</strong></p>
<ul>
<li>访问根</li>
<li>遍历左子树</li>
<li>遍历右子树</li>
</ul>
<p><strong>结果:</strong></p>
<pre><code>1,2,4,5,3,6,7
</code></pre>
<p><strong>中序遍历</strong></p>
<ul>
<li>遍历左子树</li>
<li>访问根</li>
<li>遍历右子树</li>
</ul>
<p><strong>结果:</strong></p>
<pre><code>4,2,5,1,6,3,7
</code></pre>
<p><strong>后序遍历</strong></p>
<ul>
<li>遍历左子树</li>
<li>遍历右子树</li>
<li>访问根</li>
</ul>
<p><strong>结果:</strong></p>
<pre><code>4,5,2,6,7,3,1
</code></pre>
<p><strong>水平顺序遍历</strong></p>
<ul>
<li>访问根</li>
<li>在遍历级别为1时,把所有在1+1级别的元素保存在队列中</li>
<li>进入下一个级别并且访问这个级别的所有节点</li>
<li>重复执行直到所有节点完成遍历</li>
</ul>
<p><strong>结果:</strong></p>
<pre><code>1,2,3,4,5,6,7
</code></pre>
<p><strong>实现代码</strong></p>
<figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line"> * create by zhangbo on 2019/11/20 0020</span><br><span class="line"> */</span><br><span class="line">public class BinaryTreeTravelsal &#123;</span><br><span class="line"></span><br><span class="line">    /**</span><br><span class="line">     * 水平顺序遍历二叉树方法</span><br><span class="line">     *</span><br><span class="line">     * @param root</span><br><span class="line">     * @return 最坏情况下时间空间复杂度为O(n)</span><br><span class="line">     */</span><br><span class="line">    public ArrayList&lt;ArrayList&lt;Integer&gt;&gt; levelOrder(BinaryTreeNode root) &#123;</span><br><span class="line">        //嵌套一个list内部list就是一个级别下的数据,外部就是把所有级别的集合装在一个大集合里</span><br><span class="line">        ArrayList&lt;ArrayList&lt;Integer&gt;&gt; res = new ArrayList&lt;&gt;();</span><br><span class="line">        if (root == null) &#123;</span><br><span class="line">            return res;</span><br><span class="line">        &#125;</span><br><span class="line">        //链表队列,用来存储节点</span><br><span class="line">        Queue&lt;BinaryTreeNode&gt; q = new LinkedList&lt;&gt;();</span><br><span class="line">        q.offer(root);</span><br><span class="line">        //这个空就是为了完成第一个级别的数据遍历就跳到else方法里把数据装填到res中.使得一个级别的数据放在一个list中</span><br><span class="line">        q.offer(null);</span><br><span class="line">        //用来存储当前级别的数据的集合</span><br><span class="line">        ArrayList&lt;Integer&gt; curr = new ArrayList&lt;&gt;();</span><br><span class="line">        while (!q.isEmpty()) &#123;</span><br><span class="line">            BinaryTreeNode tmp = q.poll();</span><br><span class="line">            if (tmp != null) &#123;</span><br><span class="line">                curr.add(tmp.data);</span><br><span class="line">                if (tmp.left != null) &#123;</span><br><span class="line">                    q.offer(tmp.left);</span><br><span class="line">                &#125;</span><br><span class="line">                if (tmp.right != null) &#123;</span><br><span class="line">                    q.offer(tmp.right);</span><br><span class="line">                &#125;</span><br><span class="line">            &#125; else &#123;</span><br><span class="line">                ArrayList&lt;Integer&gt; c_curr = new ArrayList&lt;&gt;(curr);</span><br><span class="line">                res.add(curr);</span><br><span class="line">                //清理掉curr数据后,res中curr的引用将会被java回收,所以不得不新建一个arraylist来装CURR</span><br><span class="line">                curr.clear();</span><br><span class="line">                if (!q.isEmpty()) &#123;</span><br><span class="line">                    q.offer(null);</span><br><span class="line">                &#125;</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">        return res;</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>





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